2. Tutorial: learning Kwant through examples

• 2.1. Introduction
  • Quantum transport
  • The Python programming language
  • Kwant
• 2.2. First steps: setting up a simple system and computing conductance
  • Discretization of a Schrödinger Hamiltonian
  • Transport through a quantum wire
  • Building the same system with less code
  • Tips for organizing your simulation scripts
• 2.3. More interesting systems: spin, potential, shape
  • Matrix structure of on-site and hopping elements
  • Spatially dependent values through functions
  • Nontrivial shapes
• 2.4. Beyond transport: Band structure and closed systems
  • Band structure calculations
  • Closed systems
• 2.5. Beyond square lattices: graphene
• 2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries
• 2.7. Computing local quantities: densities and currents
  • Introduction
  • Local densities
  • Local currents
  • Spatially varying operators
  • Defining operators over parts of a system
    • Density of states in a circle
    • Current flowing through a cut
  • Advanced Topics
    • Using bind for speed
• 2.8. Plotting Kwant systems and data in various styles
  • 2D example: graphene quantum dot
  • 3D example: zincblende structure
• 2.9. Calculating spectral density with the kernel polynomial method
  • Introduction
  • Calculating the density of states
    • Global spectral densities using random vectors
    • Local spectral densities using local vectors
  • Increasing the accuracy of the approximation
  • Calculating the spectral density of an operator
    • Spectral density with random vectors
  • Calculating Kubo conductivity
  • Advanced topics
    • Custom distributions of vectors
    • Reproducible calculations
    • Defining operators as sesquilinear maps
• 2.10. Discretizing continuous Hamiltonians
  • Introduction
  • Discretizing by hand
  • Using discretize to obtain a template
  • Building a Kwant system from the template
  • Models with more structure: Bernevig-Hughes-Zhang
  • Limitations of discretization
  • Advanced topics
• 2.11. Adding magnetic field
  • Computing Landau levels in a harmonic oscillator basis
    • Comparing with tight-binding
    • Discretizing 3D models
• 2.12. Frequently asked questions
  • What is a system, and what is a builder?
  • What is a site?
  • What is a hopping?
  • What is a site family, and what is a tag?
  • What is a lattice?
  • When plotting, how to color the different sublattices differently?
  • How to create many similar hoppings in one go?
  • How to set the hoppings between adjacent sites?
  • How to make a hole in a system?
  • How to access a system’s sites?
  • How to use different lattices for the scattering region and a lead?
  • How to cut a finite system out of a system with translational symmetries?
  • How does Kwant order the propagating modes of a lead?
  • How does Kwant order scattering states?
  • How does Kwant order components of an individual wavefunction?